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If 4<(7-x)/3, which of the following must be true?

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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 12 Feb 2018, 12:02
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III


Simplifying the given inequality we have:

4 < (7 - x)/3

12 < 7 - x

5 < -x

-5 > x

Since x is less than -5, we see that |x+3| > 2.

Also, since x < -5, we see that x + 5 will always be negative and thus -(x+5) will always be positive.

Answer: D
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If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 05 May 2018, 06:09
Bunuel wrote:
SOLUTION

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive


(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Note that we are asked to determine which MUST be true, not could be true.

\(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\).

Basically the question asks: if \(x<-5\) which of the following is true?

I. \(5<x\) --> not true as \(x<-5\).

II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true.

Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true.

III. \(-(x+5)>0\) --> \(x<-5\) --> true.

Answer: D.



Bunuel if the question asks: if \(x<-5\) which of the following is true?

how can \(|x+3|>2\), this inequality hold true for BOTH cases ? :?

you write "when \(x+3>2\), so when \(x>-1\) "

so if \(x>-1\) how can it hold true when \(x<-5\) So if \(x < -5\) then \(x\) can be -6, -7 -8 , -9 etc all negative numbers starting from -6 , whereas \(x>-1\) means thar x can be 0, 1, 3, 4 etc all positive numbers

can you explain this part, please :)
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 05 May 2018, 11:00
1
dave13 wrote:
Bunuel wrote:
SOLUTION

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive


(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Note that we are asked to determine which MUST be true, not could be true.

\(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\).

Basically the question asks: if \(x<-5\) which of the following is true?

I. \(5<x\) --> not true as \(x<-5\).

II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true.

Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true.

III. \(-(x+5)>0\) --> \(x<-5\) --> true.

Answer: D.



Bunuel if the question asks: if \(x<-5\) which of the following is true?

how can \(|x+3|>2\), this inequality hold true for BOTH cases ? :?

you write "when \(x+3>2\), so when \(x>-1\) "

so if \(x>-1\) how can it hold true when \(x<-5\) So if \(x < -5\) then \(x\) can be -6, -7 -8 , -9 etc all negative numbers starting from -6 , whereas \(x>-1\) means thar x can be 0, 1, 3, 4 etc all positive numbers

can you explain this part, please :)


I tried to explain this here: https://gmatclub.com/forum/if-4-7-x-3-w ... l#p1465124 and here: https://gmatclub.com/forum/if-4-7-x-3-w ... l#p1991132

For more on this kind of questions check Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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Re: If 4<(7-x)/3, which of the following must be true?  [#permalink]

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New post 05 Aug 2018, 05:05
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Problem Solving
Question: 156
Category: Algebra Inequalities
Page: 82
Difficulty: 600


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4<(7-x)/3
which leads to relation: x<-5
i)5<x which isn't true
ii) x<-5
x+3<-2 hence |x+3|>2
choice ii is correct
iii)x<-5
x+5<0
-(x+5)>0
choice iii is correct
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Re: If 4<(7-x)/3, which of the following must be true? &nbs [#permalink] 05 Aug 2018, 05:05

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